A class of implicit advanced step-point methods with a parallel feature for the solution of stiff initial value problems

Authors:
G. Psihoyios
Affiliations:
-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2004

Citing 4
Cited 3

Two FORTRAN packages for assessing initial value methods

ACM Transactions on Mathematical Software (TOMS)
An MEBDF code for stiff initial value problems

ACM Transactions on Mathematical Software (TOMS)
Parallel methods for initial value problems

Applied Numerical Mathematics - Special issue: parallel methods for ordinary differential equations
Parallel Solution of Ordinary Differential Equations

IEEE Transactions on Computers

A general formula for the stability functions of a group of implicit advanced step-point (IAS) methods

Mathematical and Computer Modelling: An International Journal
A new trigonometrically-fitted sixth algebraic order P-C algorithm for the numerical solution of the radial schrödinger equation

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The EAS3 multistep approach as part of explicit advanced step-point (EAS) methods

Journal of Computational Methods in Sciences and Engineering

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Abstract

In this paper, a class of implicit advanced step-point methods that possesses a parallel feature is presented. Their accuracy and stability characteristics are examined in some detail and an experimental nonparallel code has been developed in order to give us a fair indication of their capabilities. Our aim is not to discuss a ''parallel implementation'' but, to demonstrate the worthiness of the new methods. The experimental code is compared with the powerful MEBDF code on the stiff DETEST problem set and the statistics displayed are obtained from the DETEST evaluation package. Some initial conclusions concerning the efficiency of the new methods are drawn from the analysis of the numerical results.